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A347434 E.g.f.: exp( exp(x) * (exp(x) - 1 - x - x^2 / 2) ). 2
1, 0, 0, 1, 5, 16, 52, 274, 1990, 14354, 99704, 730225, 6061013, 56151330, 551040830, 5597109717, 59324775741, 664973687438, 7891158217876, 98253448977890, 1273082291906394, 17124091446383666, 239333235895599762, 3476600533730954761, 52394273274018321421 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

COMMENTS

Exponential transform of A002662.

LINKS

Table of n, a(n) for n=0..24.

FORMULA

a(0) = 1; a(n) = Sum_{k=1..n} binomial(n-1,k-1) * A002662(k) * a(n-k).

MAPLE

a:= proc(n) option remember; `if`(n=0, 1, add(

      a(n-j)*binomial(n-1, j-1)*(2^j-j*(j+1)/2-1), j=1..n))

    end:

seq(a(n), n=0..24);  # Alois P. Heinz, Sep 02 2021

MATHEMATICA

nmax = 24; CoefficientList[Series[Exp[Exp[x] (Exp[x] - 1 - x - x^2/2)], {x, 0, nmax}], x] Range[0, nmax]!

a[0] = 1; a[n_] := a[n] = Sum[Binomial[n - 1, k - 1] (2^k - 1 - k (k + 1)/2) a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 24}]

CROSSREFS

Cf. A002662, A006505, A055882, A143405, A347432, A347435.

Sequence in context: A007343 A274492 A147536 * A173871 A108300 A041469

Adjacent sequences:  A347431 A347432 A347433 * A347435 A347436 A347437

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Sep 02 2021

STATUS

approved

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Last modified January 21 00:46 EST 2022. Contains 350473 sequences. (Running on oeis4.)